Let the internal radius of dome = r m
Internal surface area of dome = 2πr²
cost of white washing at the rate of Rs 2 = 2πr² × Rs 2 = Rs 4πr²
⇒ Rs 4πr = Rs 498.96
⇒ 4 × 22/7 × r² = 498.96
⇒ r² = (498.96×7)/4×22) = 39.69
⇒ r = √39.69 = 6.3 m
Therefore, the internal surface of dome = 2πr²
= 2 × 22/7 × (6.3)2
= 2 × 22/7 × 6.3 × 6.3
= 2 × 22 × 0.9 × 6.3
= 249.98 m²
Hence, the inside surface area of the dome is 249.48 m².
(II) Volume of the air inside the dome = 2/3πr³
= 2/3 × 22/7 × (6.3)³
= 2/3 × 22/7 × 6.3 × 6.3 × 6.3
= 2 × 22 × 0.3 × 6.3 × 6.3
= 523.9 cm³
Hence, the volume of the air inside the dome is 523.9 cm³.